ABSTRACT
This article deals with railway track geometry in horizontal and vertical directions, and its measurement by means of track recording vehicle. The first part of the article introduces the mathematics tools for describing planar curves, mainly the “transformed curve” defined as the double integration of the algebraic local curvature, function of the curvilinear abscissa. The complete non linear model of the non-centered versine apparatus has been calculated in this space, as well as its simplification in the case of low local angular values. The main contribution of this article lies in the choice of algebraic local curvature as system input for the further inversion of experimental data. The following part describes the deconvolution procedure using the Wiener approach; therefore the optimal inverse filter becomes the multiplication of the direct inversion by a regularization function linked to the signal-to-noise ratio. Then, the direct modelling of the French Mauzin measurement system and the adapted inverse numerical filtering (in horizontal and vertical directions) are calculated. It is shown that the inverse procedure allows the deconvolution of track irregularities of up to 150m wavelengths.
